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A089809

Complement of A078588.

0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1

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OFFSET

1,1

COMMENTS

a(n) = 1 if (fractional part of n*r) < 1/2, else a(n) = 0, where r = golden ratio = (1 + sqrt(5))/2. - Clark Kimberling, Dec 27 2016

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 if A078588 = 0; otherwise, not.

a(n) = 1 iff A024569 is not 1.

a(n) = 1 iff A089808 is 1.

a(n) = 1 if (fractional part of n*r) < 1/2, else a(n) = 0. - Clark Kimberling, Dec 27 2016

EXAMPLE

1. a(7) = 1 since A078588(7) = 0

2. a(7) = 1 since A024569 is not 1 (A024569(7) = 3).

3. a(7) = 1 since A089808(7) = 1.

MATHEMATICA

r = GoldenRatio; z = 500;

Table[If[FractionalPart[n r] < 1/2, 1, 0 ], {n, 1, z}] (* A089809 *)

Table[If[FractionalPart[n r] > 1/2, 1, 0 ], {n, 1, z}] (* A078588 *)

1 - % (* A089809, Clark Kimberling, Dec 27 2016 *)

PROG

(Python)

from math import isqrt

def A089809(n): return ((n+isqrt(5*n**2))&1)^1 # Chai Wah Wu, Aug 17 2022

CROSSREFS

Cf. A078588, A024569, A089808.

Sequence in context: A368909 A285249 A269027 * A165211 A341389 A188027

Adjacent sequences: A089806 A089807 A089808 * A089810 A089811 A089812

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Nov 11 2003

STATUS

approved

URL: https://oeis.org/A089809

⇱ A089809 - OEIS